The number of graduates from the past five years working in jobs such as sales assistants and care workers has risen to 47%. This is up from 38% in 2008.
However, the report, which defined a graduate as someone with a qualification above A Level standard, said graduates in 2013 were more likely to be employed, less likely to be searching for work and less likely to be out of the labour force than jobseekers with lower qualifications or no qualifications.
Graduates with a degree in medicine or dentistry had the highest employment rate of all graduates, at 95%, followed by those with media and information studies, at 93%.
Medical graduates also had the highest median pay of £45,000 a year, and media and information studies graduates had the lowest pay (£21,000) of all subject groups.
Prime minister David Cameron said recently that he hoped students would become more "picky" about choosing a degree, because they were having to contribute more towards it.
Many students are now charged £9,000 a year to go to university although they don't start paying that back until their annual salary hits £21,000.
The ONS said people who had been to university are still more likely to find work and earn more over their career than non-graduates.
A report yesterday from the Financial Times found the earnings of recent university students (since 2008) have fallen so fast since the financial crisis that the latest graduates are earning 12% less than people who started their careers before the crash. It also said graduates owe about 60% more in student debt.
